New Plasmacutter

Giuseppe wrote:

Is this the same way how the expensive cutters work? Or are there some differences?

There are differences, quite a lot actually:
-High Voltage start uses a transformer at 50 or 60 Hz to raise the voltage to over 2000V, a huge resistor to dump some of the power and is wired directly to the electrode on one side and to the nozzle on the other side, also there is a RC filter to protect the rectifier from destruction at every arc start. Highly reliable, causes plenty of interference, especially as the nozzle/electrode get black inside and the arc is harder to start.
-High Voltage / High Frequency start uses a smaller high frequency (usually over 20 kHz) transformer and switching electronics on the primary side that creates 15000V through a sparc gap and another winding on a ferite core to witch the main electrode wire is also wound with the other side going to the nozzle, also has RC filters to protect rectifiers and a dumping resistor. Very reliable, causes huge amounts of interference, less sensitive to electrode/nozzle getting all black inside.
-Blow back start uses a spring loaded electrode that gets pushed back when the air is turned on while at the same time lets 3 to 5A of current through the electrode to the nozzle, so when the electrode retracts the sparc is created at what point the full cutting power is released. Pretty reliable, costs a lot in electrodes as they fail much faster due to current passing through a spring, less interference than both of the above.
-Scratch start uses ... well scratching the nozzle to the material to create a sparc, so it has nothing that the above machines have. Not sure about wiring as i never used one. Most probably creates more interference than BlowBack, but less than other two above.

Unclear if you want or have the StahlWerk, but either way they are nice, a friend has one for nearly a year and it is working just fine.
 www.stahlwerk-schweissgeraete.de//plasma-cutter/

StahlWerk has pilot start so it should work even from 3 or 4 or 5mm from the material.
Reasons for arc start failing:
-to low air pressure
-to high air pressure
-charred electrode and nozzle (black inside)
-nozzle and electrode not tightened/inserted properly
-nozzle touching the material
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Yes, nozzle on the pilot plasma must NOT touch the material as that will fail to start
Air pressure should be 5 to 5.5 Bar while air is running, not when air is stopped, use the built in regulator to check and adjust air.

Pictures of the machine ?
That is from vibrations for sure, but what acceleration are you using ?
Try lowering accelleration a bit, but anything under 200mm/s/s is to low for cutting thin sheets.